Sum and Product of Discrete Random Variables
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Theorem
Let $X$ and $Y$ be discrete random variables on the probability space $\left({\Omega, \Sigma, \Pr}\right)$.
Sum of Discrete Random Variables
Let $U: \Omega \to \R$ be defined as:
- $\forall \omega \in \Omega: \map U \omega = \map X \omega + \map Y \omega$
Then $U$ is also a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.
Product of Discrete Random Variables
Let $V: \Omega \to \R$ be defined as:
- $\forall \omega \in \Omega: \map V \omega = \map X \omega \map Y \omega$
Then $V$ is also a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.